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(a+1)/b , (b+1)/c , (a+1)/b are integers (2018 Auckland MO J5)
(a+1)/b , (b+1)/c , (a+1)/b are integers (2018 Auckland MO J5)
Source:
November 14, 2021
number theory
Integers
Problem Statement
Find all possible triples of positive integers,
a
,
b
,
c
a, b, c
a
,
b
,
c
so that
a
+
1
b
\frac{a+1}{b}
b
a
+
1
,
b
+
1
c
\frac{b+1}{c}
c
b
+
1
and
c
+
1
a
\frac{c+1}{a}
a
c
+
1
are also integers.
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